Various objects including, for example, the interior region and organs of the human body, are known to have inhomogeneous electrical properties which may be defined in terms of conductivity and dielectric constant. Information concerning the electrical properties of human tissue may be of significant clinical value. For example, conductivity differences may indicate the presence of pulmonary edema and differences in dielectric constant may indicate the presence of breast tumors. See the following references:
1. R. P. Henderson and J. G. Webster, An impedance camera for spatially specific measurements of the thorax, IEEE Trans. Biomedical Eng., BME-35, pp 250-254, May 1978. PA0 2. Sollish B. D., Drier Y, Hammerman E., Moshitzky M., Frei E. H. and Man B. A dielectric breast scanner, Digest of the XII International Conference on Medical and Biological Engineering and the V International Conference on Medical Physics, Jerusalem, Israel, August, 1979. Lecture 30.3. PA0 3. H. Schomberg, Reconstruction of spatial resistivity distribution of conducting objects from external resistance measurements, Applied Analyses and Mathematical Physics, T-41-T-42 (1979). PA0 4. M. Tasto and H. Schomberg, Object reconstruction from projections and some non-linear extension, in Pattern Recognition and Signal Processing, edited by C. H. Chen, 1978. PA0 5. H. Schomberg, Nonlinear image reconstruction from projections of ultrasonic travel times and electric current densities, Proc. Conf. on Mathematical Aspects of Computerized Tomography (Mathematisches Forschungsinstitut, Oberwolfach, Black Forest, F.R.G.) February 1980.
Were it not a matter of treatment of the human body, it might be practical to measure the electrical properties of tissue by implanting a suitable electrode internally. Such a technique is clearly impractical. Therefore it is necessary to determine the electrical properties of internal tissue on the basis of electrical measurements performed on the surface of the body.
A method and a device for measuring the electrical properties of internal human tissue by means of external measurements is proposed in U.K. patent application No. 2,019,579, published on Oct. 31, 1979 and is discussed in the following references:
The apparatus and techniques described in the above cited U.K. patent application and in the above references employ a pair of electrode arrays disposed on opposite sides of a water tank. One of the electrodes is a continuous plate electrode, while the other is an array of a plurality of small electrodes arranged in a plane opposite the first electrode on the opposite side of the object to be examined. A current meter is connected to each of the small electrodes. A potential difference is imposed between the two opposite sides and the currents are measured.
The information obtained by measurement of the currents passing through the individual small electrodes is process in the following manner: An initial guess of the conductivity distribution of the object is made and for this purpose the resistances along straight current paths, referred to in the references as "tubes of flow" are calculated. These computed resistance values are compared with the measured values and the original estimate is corrected by backprojecting the differences along the calculated current paths, which are in fact curved, rather than straight current paths as originally postulated.
Since the number of resistances is greater than the number of measurements, the water tank is rotated around the body and data processing is done once again, using the corrected estimate as the base estimate. This process continues until a desired convergence is attained.
The technique described above is an adaptation of conventional X-ray tomographic techniques. It is believed by applicants to be an unfortunate and inappropriate adaptation for the following reasons:
The technique of "tubes of flow" is suitable for X-ray propagation since it is essentially straight-line propagation. It is not suitable for electrical currents since current does not flow in a straight line in tissue. Instead, the current flow is extremely complicated and cannot be analyzed in terms of tubes of flow or stream lines.
The failure of the proposed apparatus and technique described in the aforesaid U.K. patent application is admitted by one of the inventors therein, H. Schomberg, where he writes in reference (5) as follows: "We conclude that EC-CT as presented here is impracticable. It might be possible to enforce uniqueness by restricting the class of admissible functions or by complicating experiment and model. The first way is likely to deprive EC-CT of its potential applications. The second way will probably make the practical inverse problem unmanageable. In both cases, the difficulties caused by the insensitivity of the current density to changes in the resistivity hold on. The author therefore doubts that EC-CT based on projections of the current density will ever become a practicable, quantitative imaging method".
In summary, the major difficulty of the proposed prior art apparatus is that it employs methods of analysis useful in X-ray tomography for analysing electrical properties. The difference between X-ray tomography and current measurements is that in the X-ray technique, the straight line nature of the flow makes the analysis simpler.
An additional difficulty in the proposed prior art apparatus is that there the information is analyzed in two dimensional cross sections in order to simplify the analysis. This simplification ignores important information which is present outside of the two dimensional slice since the current flow paths are not generally planar.
As a result of the direction of the proposed prior art apparatus towards straight current flows, the available permutations of voltage distributions on the electrodes are extremely limited, thus limiting the efficiency of data collection.